A) \[{{p}^{-1}}\] and \[{{r}^{2}}\]
B) \[p\] and \[{{r}^{-2}}\]
C) \[{{p}^{2}}\] and \[{{r}^{-3}}\]
D) \[p\] and \[{{r}^{-3}}\]
Correct Answer: D
Solution :
Electric field due to a dipole at bisector or at a point on its broad side on position is given by \[E=\frac{1}{4\,\pi {{\varepsilon }_{0}}}.\frac{p}{{{r}^{3}}}\] or \[E\propto \,\,\frac{p}{{{r}^{3}}}\] ....(i) where r is the distance of that point from centre of dipole. So, from Eq. (i) \[E\propto \,p\] and \[E\propto \,{{r}^{-3}}\] Note: The electric field due to a dipole at its end on position is twice the value at its broad side on position i.e., \[{{E}_{end-on}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\cdot \frac{2p}{{{r}^{3}}}\]
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